Question

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a

0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?

71
83
36
62
45
27
60
63
65
47
63
67
95
90
67

Determine the​ P-value (show steps on how to type in calculator)

Answer 1

Let denotes the population mean.

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.01 level of significance if P-value < 0.01

Now,

The value of the test statistic

P-value =

Formula in TI 83 calculator : 2* tcdf(0.566930, 9999, 14)

Since P-value > 0.01, so we fail to reject H₀ at 0.01 level of significance and we can conclude that population mean is not significantly different from 60.